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Spectral Exterior Calculus and its Implementation
Get PDFPreserving geometric, topological and algebraic structures at play in partial differential equations has proven to be a fruitful guiding principle for computational methods in a variety of scientific fields. However, structure-preserving numerical methods have traditionally used spaces of piecewise polynomial basis functions with local support to interpolate differential forms. When solutions are known to be smooth, a spectral treatment is often preferred instead as it brings exponential convergence. While recent works have established spectral variants of discrete exterior calculus, no existing approach offers the full breadth of exterior calculus operators and a clear distinction between vectors and covectors. We present such a unified approach to spectral exterior calculus (SPEX) and provide detail on its implementation. Notably, our approach leverages Poincare duality through the use of a primal grid and its dual (with a natural handling of boundaries to facilitate the treatment of boundary conditions), and uses a twin representation of differential forms as both integrated and pointwise values. Through its reliance on the fast Fourier transform, the resulting framework enables computations in arbitrary dimensions that are both efficient and have excellent convergence properties
Covalent Functionalization of Metal-Oxide Surfaces with Non-Traditional Ligands
Get PDFHerein detailed are the syntheses, properties, and applications of metal-oxide nanosubstrates
covalently functionalized with two classes of materials, inorganic macrocycles called
corroles, and genomic deoxyribonucleic acid (DNA). These products have found biomedical
applications in tumor imaging and chemotherapeutic sequestration, respectively. Both
classes of prepared materials are the first of their kind.
Corroles are tetrapyrrolic macrocycles, which have found applications in tumor imaging and
treatment, catalysis, solar fuels, and energy conversion. The direct functionalization of
metal-oxides with inorganic macrocycles, including corroles, has largely revolved around
the formation of hydrogen bonding type interactions between the substrate and the ligand.
Hydrogen bonding motifs result in materials with only moderate stability due to solvent
dissolution. In the first three chapters of this thesis, the scalable preparation of 5,10,15-
(trispentafluorophenyl) corrole and its subsequent covalent functionalization of metal-oxide
surfaces are discussed.
Chapter 1 details mechanistic elements of the oligomerization and oxidative cyclization of
5,10,15-(trispentafluorophenyl) corrole from pentafluorobenzaldehyde and pyrrole. Prior to
this work the synthesis of triperfluoroaryl corroles was dangerously exothermic and could
only be carried out on milligram scale. Mechanistic insights led to a safe and scalable
synthesis of the desired corrole species, achieving a 17.0 % yield (4.58 g). A detailed
discussion of the covalent functionalization of the surface of TiO2 with chlorosulfonated
derivatives of 5,10,15-tris(pentafluorophenyl) corrole is presented in Chapter 2. The
chlorosulfonated species investigated include the freebase, gallium, and aluminum corroles.
Hydroxyl groups on the metal-oxide react with the chlorosulfonyl groups of the corrole ring
via nucleophilic attack, resulting in the formation of sulfonic ester linkages. The aluminum
species was further investigated as a potential near-infrared optical contrast agent. The
details of this study, described in Chapter 3, include imaging experiments with immortalized
human cancer lines and harvested mouse hepatocytes. This nanoconjugate exhibited low
toxicity and efficient cellular uptake.
Conventional chemotherapy agents that target DNA are notorious for producing severe
side-effects. Sequestering chemotherapeutics that enters systemic circulation, in a process
deemed “ChemoFiltration,” is a strategy for reducing off-target toxicity. Materials capable
of such activity have yet to be fully realized. Reported in Chapter 4 are the first methods
covalent attachments of genomic DNA to surfaces, namely magnetite (Fe3O4) nanoparticles,
via two separate strategies. These materials show efficacy in removing doxorubicin,
cisplatin, and epirubicin from biologically relevant solutions. A device coated with this
material demonstrated in vivo activity in a porcine model.</p
Boosting Boosting
Get PDFMachine learning is becoming prevalent in all aspects of our lives. For some applications, there is a need for simple but accurate white-box systems that are able to train efficiently and with little data.
"Boosting" is an intuitive method, combining many simple (possibly inaccurate) predictors to form a powerful, accurate classifier. Boosted classifiers are intuitive, easy to use, and exhibit the fastest speeds at test-time when implemented as a cascade. However, they have a few drawbacks: training decision trees is a relatively slow procedure, and from a theoretical standpoint, no simple unified framework for cost-sensitive multi-class boosting exists. Furthermore, (axis-aligned) decision trees may be inadequate in some situations, thereby stalling training; and even in cases where they are sufficiently useful, they don't capture the intrinsic nature of the data, as they tend to form boundaries that overfit.
My thesis focuses on remedying these three drawbacks of boosting.
Ch.III outlines a method (called QuickBoost) that trains identical classifiers at an order of magnitude faster than before, based on a proof of a bound. In Ch.IV, a unified framework for cost-sensitive multi-class boosting (called REBEL) is proposed, both advancing theory and demonstrating empirical gains. Finally, Ch.V describes a novel family of weak learners (called Localized Similarities) that guarantee theoretical bounds and outperform decision trees and Neural Nets (as well as several other commonly used classification methods) on a range of datasets.
The culmination of my work is an easy-to-use, fast-training, cost-sensitive multi-class boosting framework whose functionality is interpretable (since each weak learner is a simple comparison of similarity), and whose performance is better than Neural Networks and other competing methods. It is the tool that everyone should have in their toolbox and the first one they try.</p
Immersing Essential Surfaces in Odd Dimensional Closed Hyperbolic Manifolds
Get PDFThe surface subgroup theorem, proved by Kahn and Markovic, states that the fundamental group of every closed hyperbolic 3-manifold contains a closed hyperbolic surface subgroup. The criterion of incompressibility, a criterion to ensure that an immersing surface to be essential, has played an important role in their proof.
In this thesis, we generalize the criterion of incompressibility from dimension three to all higher dimensions. Then we use the mixing property of the geodesic flow to construct a closed immersed surface which satisfies the assumption of our criterion when the hyperbolic manifold is in an odd dimension. Together, we prove the surface subgroup theorem in all odd dimensions.</p
Targeting DNA Mismatches with Luminescent Ruthenium Complexes
Get PDFDNA base pair mismatches occur naturally in cells, typically as a result of errors during replication. Cells have evolved a DNA damage response pathway called mismatch repair (MMR) that identifies and corrects base pair mismatches in newly synthesized DNA. However, proteins involved in MMR can undergo mutations, rendering them incapable of correcting mismatches. Such deficiencies in MMR leads to an increase in genetic mutations and are associated with several forms of cancer. Because a higher mismatch frequency serves as an early indicator of cancer progression, DNA mismatches are a promising target in the design of small molecule therapeutics and diagnostics. In this context, transition metal complexes are prime candidates, owing to their valuable spectroscopic and photophysical properties and versatile coordination sphere geometries. Our laboratory focuses on generating octahedral rhodium and ruthenium complexes that selectively target DNA mismatches. A class of rhodium complexes bearing sterically expansive planar ligands bind DNA mismatches with high selectivity and exhibit preferential cytotoxicity towards MMR-deficient cancer cells. These compounds bind to DNA through metalloinsertion, in which the bulky ligand inserts into the duplex at the thermodynamically destabilized mismatch site, displacing the mismatched bases into the DNA groove.
Herein we describe recent advances in the development of luminescent ruthenium complexes that selectively probe DNA mismatches. We demonstrate that [Ru(Me4phen)2(dppz)]2+ (Me4phen = 3,4,7,8-tetramethyl-1,10-phenanthroline; dppz = dipyrido[3,2-a:2’,3’-c]phenazine) is a DNA “light switch” that exhibits a significantly brighter steady-state emission in the presence of a DNA duplex containing a mismatch relative to completely well-matched DNA. Importantly, the bulky Me4phen ancillary ligands discourage deep intercalation of dppz between well-matched base pairs, and instead, [Ru(Me4phen)2(dppz)]2+ favors metalloinsertion at thermodynamically destabilized mismatches. [Ru(Me4phen)2(dppz)]2+ possesses a higher binding affinity towards a DNA mismatch relative to well-matched base pairs, and furthermore exhibits a longer excited-state emission lifetime when bound to a mismatch compared to that when intercalated at well-matched sites; both of these observations contribute to the dramatic steady-state emission enhancement detected with the mismatched DNA duplex. Additionally, we reveal that the right-handed delta (∆) isomer of [Ru(Me4phen)2(dppz)]2+ is the enantiomer which imparts all mismatch selectivity, consistent with the handedness of B-form DNA.
Another mismatch-specific luminescent probe presented in this work is [Ru(bpy)2(BNIQ)]2+ (bpy = 2,2’-bipyridine; BNIQ = benzo[c][1,7]naphthyridine-1-isoquinoline). In contrast to [Ru(Me4phen)2(dppz)]2+, the BNIQ complex exploits a bulky inserting ligand that selectively undergoes metalloinsertion at a DNA mismatch. This compound too exhibits a brighter steady-state emission in the presence of a mismatched duplex compared to entirely well-matched DNA, which we attribute to the fact that [Ru(bpy)2(BNIQ)]2+ possesses nearly a 500-fold higher binding affinity for the mismatch site compared to well-matched base pairs. Taken together, [Ru(Me4phen)2(dppz)]2+ and [Ru(bpy)2(BNIQ)]2+ represent two different yet valid approaches in the rational design of mismatch-specific small molecules, one based on ancillary ligand functionalization and the other on incorporating a sterically expansive inserting ligand.
A third approach towards the design of mismatch-specific luminescent ruthenium probes that is briefly explored here is the modification of the intercalating dppz ligand of [Ru(bpy)2(dppz)]2+. Bearing a dppz ligand substituted with four methyl groups, [Ru(bpy)2(tmdppz)]2+ (tmdppz = 3,4,7,8-tetramethyl dipyridophenazine) shows no luminescence discrimination between mismatched and well-matched duplexes. This observation ostensibly arises from the fact that the appended methyl groups shield the dppz phenazine nitrogen atoms from interactions with water when intercalated within the DNA.
With mismatch-specific luminescent metalloinsertors such as [Ru(Me4phen)2(dppz)]2+ in hand, we have commenced biological investigations to see whether these compounds can serve as luminescent proxies for rhodium metalloinsertors in MMR-deficient cancer cells. Confocal microscopy of HCT116N and HCT116O cells reveals that [Ru(Me4phen)2(dppz)]2+ does preferentially localize to mitochondria, unlike potent cell-selective rhodium complexes such as [Rh(chrysi)(phen)(PPO)]2+ (PPO = 2-(pyridine-2-yl)propan-2-ol; chrysi = 5,6-chrysenequinone diimine); however, [Ru(Me4phen)2(dppz)]2+ shows some degree of nuclear entry. Here our goal is the application of the mismatch-specific luminescent probe in co-localization experiments to investigate what proteins are involved in the DNA damage response that is activated upon metalloinsertor binding in cellulo.
The work presented here expands beyond the study of luminescent ruthenium complexes. Amino acid conjugates of the earlier-generation rhodium metalloinsertor [Rh(HDPA)2(chrysi)]3+ (HDPA = 2,2’-dipyridylamine) were synthesized. While these conjugates exhibit mismatch binding affinities comparable to other rhodium metalloinsertors, they lose cell-selective biological activity, which may arise from altered uptake and/or sub-cellular localization. Finally, preliminary investigations were conducted on [Re(CO)3(pyOEt)(dppn)]+ (pyOEt = ethyl 3-(pyridin-4-yl)propanoate; dppn = benzodipyridophenazine) and [Ru(CN)(tpy)(dppz)]+ (tpy = terpyridine; CN = cyano), which were designed as IR-active probes to study the kinetics of DNA-mediated charge transport (CT) by time-resolved infrared (TRIR) spectroscopy. While these complexes do not possess the desired spectral TRIR properties as originally intended, steady-state luminescence experiments do suggest that this donor-acceptor pair is capable of undergoing DNA-mediated electron transfer.
Altogether, this work demonstrates the versatility of transition metal complexes as non-covalent probes for DNA. Importantly, through the rational modification of their three-dimensional ligand scaffold, one can achieve site-specific recognition of clinically relevant biomarkers such as DNA mismatches.</p
The Architecture of the Nuclear Pore Complex
Get PDFNucleocytoplasmic transport, the regulated trafficking of macromolecules in and out of the nucleus, occurs primarily through nuclear pore complexes (NPCs). NPCs are massive macromolecular machines embedded in the nuclear envelope which generate ~40 nanometer transport channels to facilitate transport. Because of its size and complexity (~1000 subunits, ~120 MDa), the structure of the NPC has remained poorly understood. This thesis presents a bottom-up approach to understanding the structure and function of the NPC through reconstitution of the proteins and structural and biochemical studies. The first three chapters present work towards determining the composite structure of the symmetric core of the NPC. X-ray crystal structures are described for many of the components of the symmetric core. This includes a heterohexameric coat nucleoporin complex containing Nup120, Nup85, Nup145C, Sec13, Seh1, and Nup84, revealing how these proteins assemble into one of the main subcomplexes in the NPC. Reconstitution of the symmetric core components and analysis of the protein-protein interaction between the components provides a detailed biochemical map for the protein interaction network in the NPC. X-ray crystal structures of overlapping fragments facilitate the generation of accurate atomic model for full-length proteins. An iterative, sequential docking approach is developed to dock these models into a cryoelectron tomographic reconstruction of the human NPC, yielding a composite model for the structure of the symmetric core of the NPC. In the next two chapters, this analysis is extended to the cytoplasmic-specific decorations of the NPC. The structure of the C-terminal domain of Nup358 is reported and its catalytic activity is described. Lastly, reconstitution of human DDX19 activation by the NPC reveals mechanistic insight into how the NPC directly regulates the last step of mRNA export
Acid-Stable Electrocatalysts for the Solar Production of Fuels
Get PDFSunlight is one of the few renewable resources that can meet global energy demand. Unfortunately, while solar energy has grown in the past few years, several economic and scientific constraints have hindered mass adoption. One of the main obstacles solar energy faces is the lack of economically competitive storage technologies. Artificial photosynthesis is a potential solution in which solar energy is directly converted into energy dense chemical bonds that can be easily stored and transported.
One impediment facing the commercialization of artificial photosynthesis is the use of expensive and rare precious metals as catalysts. This dissertation focuses on the achievements of the past five years in characterizing novel, earth-abundant, acid-stable hydrogen evolution catalysts. While nickel alloys have long been known as catalysts for the hydrogen evolution reaction in basic media, it has only been in the past decade that earth abundant catalysts that are stable in acidic media have been reported. These discoveries are critically important as the many proposed artificial photosynthetic devices require the use of acidic media.
In this dissertation we examine two families of hydrogen evolution catalysts: transition metal chalcogenides (namely molybdenum and cobalt selenide) as well as transition metal phosphides (cobalt phosphide). In addition to the electrochemical characterization of these catalysts, spectroscopic characterizations were performed in order to carefully examine the chemical compositions of these catalysts before, after and during the hydrogen evolution reaction. This analysis elucidated both chemical, and structural changes that occurred after the catalysts had been subject to the hydrogen evolution reaction conditions.
The final chapter in this thesis delves into the techno-economic realities of energy transportation via different fuels. Due to the strong interest in renewable energy, several future energy transportation scenarios, including 100% grid electrification and widespread installation of hydrogen pipelines, have been proposed. In order to get a fuller understanding of such potential infrastructure alternatives, we report their differing energy transportation costs.</p
Superconducting Nonlinear Kinetic Inductance Devices
Get PDFWe describe a novel class of devices based on the nonlinearity of the kinetic inductance of a superconducting thin film. By placing a current-dependent inductance in a microwave resonator, small currents can be measured through their effect on the resonator’s frequency. By using a high-resistivity material for the film and nanowires as kinetic inductors, we can achieve a large coefficient of nonlinearity to improve device sensitivity. We demonstrate a current sensitivity of 8 pA/√Hz, making this device useful for transition-edge sensor (TES) readout and other cutting-edge applications. An advantage of these devices is their natural ability to be multiplexed in the frequency domain, enabling large detector arrays for TES-based instruments. A traveling-wave version of the device, consisting of a thin-film microwave transmission line, is also sensitive to small currents as they change the phase length of the line due to their effect on its inductance. We demonstrate a current sensitivity of 5 pA/√Hz for this version of the device, making it also suitable for TES readout as well as other current-detection applications. It has the advantage of multi-gigahertz bandwidth and greater dynamic range, offering a different approach to the resonator version of the device. Finally, we also demonstrate a transmission-line resonator version of the device that combines some of the advantages of the nanowire resonator and the traveling-wave device. This version of the device has high dynamic range but can also be easily multiplexed in the frequency domain.
A lumped-element resonator similar to the first device can be placed in a loop configuration to make it sensitive to magnetic fields. We demonstrate an example of such a device whose sensitivity could ultimately reach levels similar to those of state-of-the-art DC SQUIDs, making it potentially useful for many magnetometry applications given its ease of multiplexing. Finally, a similar microwave resonator is shown to exhibit parametric gain of up to 29 dB in the presence of a strong pump tone. The noise performance of this parametric amplifier approaches the quantum limit, making it useful for applications in quantum information and metrology.</p
Thermo-Acoustic Coupling and Dynamic Response of a Premixed Methane-Air Flame
Get PDFThe work herein generally applies to the problem of combustion instability. Combustion instabilities first arose in engineering practice in the 1940s when they were experienced during the development of solid and liquid propellant rocket engines. Later, similar problems arose in gas turbine combustors and afterburners. However, the earliest technical case of the phenomenon dates back to Rijke in 1859 with his "singing" tube.
The presented work focuses on the study of a simple, stagnation plane stabilized, laminar, flat-flame burner. In particular the dynamic response of the burner is examined under excitation by a driven acoustic field. After characterization of the burner’s operational range, the response of the system is measured from 20 Hz to nearly 2000 Hz over the span of operating parameters using an optically filtered PMT and lens combination. A library of the collected and reduced data is generated.
A deeper investigation of the burner dynamics at a given reference operating condition is performed using phase-resolved PLIF. Fluctuations in the spatial distributions of the LIF signals for several target species (OH, CH, CH2O) under acoustic forcing are measured. In addition, visualization of the unsteady reactant flow using precision acetone seeding and PLIF at 277 nm is performed. Subsequent cinematographic sequences are produced along with spatially resolved plots of the combustion response function and the forced Rayleigh index for numerous drive frequencies. A library of the collected and reduced data is assembled.
Analysis of the collected data reveals two principal mechanisms contributing to the unsteady response of the flame. Structure development in (and subsequent convention along) the unsteady shear layer of the laminar jet dominates the response at the outer reaches of the flame. The inner region of the flame is driven largely by the Helmholtz response of the burner nozzle cavity. These two operations mutually contribute to produce the general shape of the combustion response curve. Ultimately, the data is used to construct a simplified model for the combustion response function. The model is enhanced with two additional revisions guided by the improved understanding of the mechanisms involved.
The document ends with numerous appendices describing, in detail, the equipment used, much of which was fabricated specifically for this work. These appendices, in combination with information presented in the chapters, provide substantial detail regarding the experimental configuration and operating conditions. Great effort was made to provide the necessary information to allow replication of the experiments as well as to support future modeling endeavors as a validation dataset.</p
Wireless Nano and Molecular Scale Neural Interfacing
Get PDFNanoscale circuits and sensors built from silicon nanowires, carbon nanotubes and other devices will require methods for unobtrusive interconnection with the macroscopic world to fully realise their potential; the size of conventional wires precludes their integration into dense, miniature systems. The same wiring problem presents an obstacle in our attempts to understand the brain by means of massively deployed nanodevices, for multiplexed recording and stimulation in vivo. We report on a nanoelectromechanical system that ameliorates wiring constraints, enabling highly integrated sensors to be read in parallel through a single output. Its basis is an effect in piezoelectric nanomechanical resonators that allows sensitive, linear and real-time transduction of electrical potentials. We interface multiple signals through a mechanical Fourier transform using tuneable resonators of different frequency and extract the signals from the system optically. With this method we demonstrate the direct transduction of neuronal action potentials from an extracellular microelectrode. We further extend this approach to incorporate nanophotonics for an all-optical system, coupled via a single optical fibre. Here, the mechanical resonators are both driven and probed optically, but modulated locally by the voltage sensors via the piezoelectric effect. Such piezophotonic nanoelectromechanical systems may be integrated with nanophotonic resonators, allowing concordant multiplexing in both the radiofrequency and optical bandwidths. In principle, this would allow billions of sensor channels to be multiplexed on an optical fibre. With view to eventually integrating such technology into a neural probe, we develop fabrication methods for crafting wired silicon neural probes via photolithography and electron beam lithography. Finally, to complement recording, we propose novel ideas for wireless, multiplexed neural stimulation through the use of radiofrequency-sensitive molecular scale resonators